New Distinguishers for Negation-Limited Weak Pseudorandom Functions

no code implementations • 23 Mar 2022 • Zhihuai Chen, Siyao Guo, Qian Li, Chengyu Lin, Xiaoming Sun

We show how to distinguish circuits with $\log k$ negations (a. k. a $k$-monotone functions) from uniformly random functions in $\exp\left(\tilde{O}\left(n^{1/3}k^{2/3}\right)\right)$ time using random samples.

Negation

Testing $k$-Monotonicity

no code implementations • 1 Sep 2016 • Clément L. Canonne, Elena Grigorescu, Siyao Guo, Akash Kumar, Karl Wimmer

Our results include the following: - We demonstrate a separation between testing $k$-monotonicity and testing monotonicity, on the hypercube domain $\{0, 1\}^d$, for $k\geq 3$; - We demonstrate a separation between testing and learning on $\{0, 1\}^d$, for $k=\omega(\log d)$: testing $k$-monotonicity can be performed with $2^{O(\sqrt d \cdot \log d\cdot \log{1/\varepsilon})}$ queries, while learning $k$-monotone functions requires $2^{\Omega(k\cdot \sqrt d\cdot{1/\varepsilon})}$ queries (Blais et al. (RANDOM 2015)).

Learning Theory